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Representation and approximation of ambit fields in Hilbert space

Benth, Fred Espen; Eyjolfsson, Heidar
Journal article; SubmittedVersion
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ambit-repr.pdf (292.5Kb)
Year
2017
Permanent link
http://urn.nb.no/URN:NBN:no-58228

CRIStin
1461212

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  • Matematisk institutt [2138]
  • CRIStin høstingsarkiv [8384]
Original version
Stochastics: An International Journal of Probability and Stochastic Processes. 2017, 89 (1), 311-347
Abstract
We lift ambit fields to a class of Hilbert space-valued volatility modulated Volterra processes. We name this class Hambit fields, and show that they can be expressed as a countable sum of weighted real-valued volatility modulated Volterra processes. Moreover, Hambit fields can be interpreted as the boundary of the mild solution of a certain first order stochastic partial differential equation. This stochastic partial differential equation is formulated on a suitable Hilbert space of functions on the positive real line with values in the state space of the Hambit field. We provide an explicit construction of such a space. Finally, we apply this interpretation of Hambit fields to develop a finite difference scheme, for which we prove convergence under some Lipschitz conditions.

This research was first published in Schochastics: An International Journal of Probability and Stochastic Processes. © Taylor & Francis.
 
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